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From my point of view, the study of quasimodes for Schroedinger operators on a compact manifold is essentially the study of how quantum mechanics can be fooled by randomness because I have shown that the universe must be compact.  Results on existence of periodic solutions of Hamiltonian systems plus the construction of quasimodes concentrating on periodic orbits is the area of connection between quantum mechanics as an approximation of classical mechanics without the construction  of ‘semiclassical approximations’ with $h$ tending to zero.  The following paper discusses construction of quasimodes near special type of geodesics.